1. Field of the Invention
The present invention is related to the field of mathematics and, more particularly, to a device for helping students visualize mathematical relationships relating to circles.
2. Description of the Related Art
Students of mathematics often have difficulty visualizing abstract terms and values, and their relationships. One such value, that of the number xcfx80, can be confusing when viewed apart from practical application. Therefore, a need exists for a way to help students better appreciate the interrelationships between n and the radius, diameter, circumference and area of a circle, by transforming an otherwise abstract numerical principle into a tangible reality.
Accordingly, it is an object of the present invention to visually demonstrate otherwise abstract mathematical relationships, particularly relating to circles.
Another object of the present invention is to demonstrate the number xcfx80 using a physical manipulative.
A further object of the present invention is to demonstrate with a tangible structure that the circumference of a circle consists of xcfx80 diameters.
Yet another object of the present invention is to physically demonstrate the area of a circle through the decomposition of the circle into a plurality of sectors which, when rearranged, approximate a parallelogram whose area is shown to be xcfx80r2.
Yet a further object of the invention is an effective classroom teaching device for concepts relating to circles that is simple in construction so as to be convenient and inexpensive to use.
The present invention, which is referred to herein as the Circle Solver, includes a combination of devices that demonstrate visually and on an intuitive level at least three essential concepts about the circle. Firstly, these devices physically demonstrate the number xcfx80. Secondly, they visually demonstrate that the circumference (C) of a circle consists of xcfx80 times the circle diameter (d), or xcfx80 diameters of the circle, namely C=xcfx80d. Thirdly, these devices physically demonstrate the area of a circle through the decomposition of the circle into approximately a parallelogram whose area is shown to be xcfx80 times the radius (r) squared, or xcfx80r2.
In a preferred embodiment, the Circle Solver includes as a first device a cylindrical container with a snug-fitting removable lid which can be used to demonstrate xcfx80 and circumference. Within the container is a second device that demonstrates a circle""s area. This second device includes a plurality of circle sectors strung together on a string that, when assembled in one particular way, form exactly one complete circle and, when arranged in another way, approximate a parallelogram.